Isogeometric Analysis vs. NURBS-Mapped Finite Elements: A Study on Selected Examples

Abstract

Isogeometric Analysis (IGA) is a numerical method that integrates finite element analysis (FEA) with CAD geometry representations using NURBS-based basis functions. In this work, we compare numerical simulations using IGA with a finite element approximation, where the geometric mapping is performed using NURBS, but the approximation space is constructed using traditional hierarchical finite element shape functions. The comparison focuses on problems with manufactured solutions involving both linear and curved geometries. Error analyses are conducted with respect to the number of degrees of freedom to assess the relative performance and accuracy of each approach.